The warfare skill tree has a lot more in it than just "swinging a weapon every turn", you'll likely be using some kind of special ability in addition to swinging, or using several abilities to deal damage.
As for the weapons, I am not sure how many axes there were in EA since I never went to look for any specifically, but it probably doesn't matter too much if you go 1 or 2 handed. You'll have to decided if you want the extra tankiness with a shield or the extra damage with either dual-wield or two-handed. You can also go with an empty off-hand and take the new "ambidextrous" talent that will allow you to throw grenades and cast scrolls for 1AP less.
I suggest you just put a point or two into a magic school if you want some utility or damage from that school, but remember that most will scale with INT and if you are planning to deal most of your damage with axe(s) then you'll likely be investing primarily in STR. Aerothurge has a number of good positioning skills (be careful not to stun yourself) and pyromancy has a number of good buff skills, neither of which would rely on INT.
The battlemage preset defaults to dual-wielding axes, +1 STR, +1 INT, +1 CON, and a point into warfare and aerothurge. This might be perfect for you if you want to really play a hybrid (just remember that you'll be dealing less physical and less magical damage than you otherwise would could be).
"Viable" is somewhat subjective, but theoretically if you take any of the presets and just run with it then that would be "viable" even if not optimised. In my opinion going too hybridised with the way things are shaping up is not worth it as you will be trying to break through both physical and magical armour at the same time, but if it synergises with your team that might not be an insurmountable obstacle.
